# Identities of the Rogers--Ramanujan--Slater Type

## TL;DR

This paper demonstrates that over half of Slater's Rogers-Ramanujan identities can be derived using three multiparameter Bailey pairs and $q$-difference equations, also discovering new identities with combinatorial interpretations.

## Contribution

It introduces a simplified method to derive many Rogers-Ramanujan type identities using Bailey pairs and $q$-difference equations, and presents new identities with combinatorial insights.

## Key findings

- Over half of Slater's identities derived using three Bailey pairs.
- New Rogers-Ramanujan type identities discovered.
- Natural combinatorial interpretations provided for many identities.

## Abstract

It is shown that (two-variable generalizations of) more than half of Slater's list of 130 Rogers-Ramanujan identities (L. J. Slater, Further identities of the Rogers-Ramanujan type, \emph{Proc. London Math Soc. (2)} \textbf{54} (1952), 147--167) can be easily derived using just three multiparameter Bailey pairs and their associated $q$-difference equations. As a bonus, new Rogers-Ramanujan type identities are found along with natural combinatorial interpretations for many of these identities.